Multiple View Geometry in Computer Vision (英語) ペーパーバック – 2004/3/25
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A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.
'I am very positive about this book. The authors have succeeded very well in describing the main techniques in mainstream multiple view geometry, both classical and modern, in a clear and consistent way.' Computing Reviews
'… a book which is timely, extremely thorough and commendably clear … Overall, the approach is masterly … The authors have managed to present the very essence of the subject in a way which the most subtle ideas seem natural and straightforward. I have never seen such a clear exploration of the geometry of vision. I would wholeheartedly recommend this book. It deserves to be in the library of every serious researcher in the field of computer vision.' Journal of Robotica
'The new edition features an extended introduction covering the key ideas in the book (which itself have been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.' Zentralblatt MATH
順序だてて「Projective Geometry」「Single View」「Two-View」「Three-View」「N-View」...と進んでいく流れは非常に読みやすく、しかも後述の問題の解法を既出問題に絡めて解説していますので、ともすれば問題が簡単に見えてしまいます。勿論専門家向けの本だとは思いますが、私のような門外漢でも頑張れば何とか読めそうに思えてしまいます（錯覚？）。数学もそれほど難しいものは使っておらず、かなりの部分が特異値分解（SVD）に帰着されます。
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The book begins with some background material on 2D and 3D geometry. Then the author explains single-view geometry and how cameras map an image in 3D space to an image. Two-view geometry is next, with the author describing the epipolar geometry of two cameras ahd projective reconstruction from resulting image map correspondences. Part three of the book extends ideas to three cameras and the resulting trifocal geometry. The final section of the book takes the algorithms of the book to N views. Thus this book has a simple and straightforward structure that belies the complexity of the material.
If you are really researching this subject you should probably have this book for explanation, illustrations, and rigor, and the Invitation book for enlightenment through a good example-based approach. You should also have Introductory Techniques for 3-D Computer Vision as a text on the individual pieces of algorithms involved in 3D vision. And don't even think about getting into this subject unless you already have a firm foundation in linear algebra, image processing, and computer vision in general as found in Computer Vision, which is my favorite introductory computer vision text.
Have you ever wondered why 4x4 matrices are used in computer graphics? In school we got a half-way answer about the projective matrix, but it was never really satisfying. This book explains the math behind that and much more clearly, leaving you with many "ah ha" moments.
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